Understanding Slope and Intercept in Linear Costs

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write a linear equation to represent the total cost (C) in terms of miles driven (m). What is the slope and what does it represent?

• C = 20 + 0.50m; slope = 0.50, representing the cost per mile.

• C = 20 - 0.50m; slope = -0.50, representing a discount per mile.

• C = 0.50m; slope = 0.50, representing the cost without the flat fee.

• C = 20 + 1.00m; slope = 1.00, representing the total cost of the car rental.

If you graph the equation from the previous problem, what are the coordinates of the y-intercept? What does this point represent in the context of the problem?

• (0, 0) where y is the value of the independent variable at x=0.

• (x, 0) where x is the value of the dependent variable at y=0.

• (0, y) where y is the maximum value of the dependent variable.

• (0, y) where y is the value of the dependent variable at x=0.

A local bakery sells cupcakes for $3 each and charges a delivery fee of $5. Write a linear equation for the total cost (C) based on the number of cupcakes (x) purchased. What is the slope and what does it represent?

• C = 3x; Slope = 0

• C = 3x + 5; Slope = 3

• C = 2x + 5; Slope = 2

• C = 5x + 3; Slope = 5

Using the equation from the previous problem, graph the linear equation. What is the y-intercept and what does it signify in this scenario?

• The y-intercept is the value of y when x=0, signifying the initial condition of the scenario.

• The y-intercept is the point where the line crosses the x-axis, showing the maximum value in the scenario.

• The y-intercept is the slope of the line, representing the rate of change in the scenario.

• The y-intercept is the value of x when y=0, indicating the final outcome of the scenario.

A gym charges a monthly membership fee of $30 plus $10 for each class attended. Write the linear equation for the total cost (C) based on the number of classes (c) attended. What is the slope?

• C = 30 + 5c; slope = 5

• C = 30 + 10c; slope = 10

• C = 20 + 10c; slope = 20

• C = 30 + 15c; slope = 15

If you were to graph the equation from the previous problem, what would the x-intercept represent in the context of gym membership?

• The total revenue generated from all memberships.

• The number of gym locations available.

• The average duration of a gym membership.

• The number of memberships sold when revenue is zero.

A phone company offers a plan that costs $25 per month plus $0.10 per text message. Write a linear equation for the total cost (C) based on the number of text messages (t) sent. What is the slope?

• The slope is 0.25.

• The slope is $0.05.

• The slope is 1.00.

• The slope is 0.10.

Graph the equation from the previous problem. What does the y-intercept represent in this context?

• The y-intercept represents the initial value of y when x is zero.

• The y-intercept shows the maximum value of y.

• The y-intercept represents the average value of y over all x.

• The y-intercept indicates the slope of the line.

A school is selling tickets for a play at $8 each, with a fixed cost of $50 for the venue. Write a linear equation for the total revenue (R) based on the number of tickets (n) sold. What is the slope?

• R = 5n; slope = 5

• R = 8n + 50; slope = 50

• R = 50 + 8n; slope = 50

• R = 8n; slope = 8

Using the equation from the previous problem, if you graph it, what does the x-intercept tell you about the ticket sales?

• The x-intercept shows the maximum ticket sales possible.

• The x-intercept represents the total cost of the tickets.

• The x-intercept indicates the break-even point for ticket sales.

• The x-intercept indicates the number of tickets sold at a loss.